Lecture 02: OR Modeling

Approach

Bangladesh University of Eng. & Tech. Slide 1 of 15 Industrial &Production Engineering

 The Usual Phases of an OR Study

1. Define the problem of interest and gather relevant data.

2. Formulate a mathematical model to represent the
problem.
3. Develop a computer-based procedure for deriving
solutions to the problem from the model.
4. Test the model and refine it as needed.
5. Prepare for the ongoing application of the model as
prescribed by management.
6. Implement.

Bangladesh University of Eng. & Tech. Slide 2 of 15 Industrial &Production Engineering

 Defining problem and gathering data

• Most practical problems encountered by OR teams are

initially described in a vague, imprecise way.
• First step is to study the relevant system and develop a
well-defined statement of the problem to be considered.
– Determine such things as the appropriate objectives, constraints,
interrelationships, possible alternative courses of action, time
limits for making a decision, and so on.

• The OR team normally works in an advisory capacity.

• Ascertaining the appropriate objectives is a very
important aspect of problem definition.
• OR is concerned with the welfare of the entire
organization.
Bangladesh University of Eng. & Tech. Slide 3 of 15 Industrial &Production Engineering
 Defining problem and gathering data

• An OR study seeks solutions that are optimal for the

overall organization rather than suboptimal solutions that
are best for only one component.
• For profit-making organizations, one possible approach
to circumventing the problem of suboptimization is to use
long-run profit maximization (considering the time value
of money) as the sole objective.

Bangladesh University of Eng. & Tech. Slide 4 of 15 Industrial &Production Engineering

 Defining problem and gathering data

• Five parties generally affected by a business firm located

in a single country are:
(1) the owners (stockholders, etc.),
(2) the employees,
(3) the customers,
(4) the suppliers, and
(5) the government and hence the nation.

Bangladesh University of Eng. & Tech. Slide 5 of 15 Industrial &Production Engineering

Defining problem and gathering data

• OR teams typically spend a surprisingly large amount of

time gathering relevant data about the problem.
• It often is necessary to install a new computer-based
management information system to collect the necessary
data on an ongoing basis and in the needed form.

Bangladesh University of Eng. & Tech. Slide 6 of 15 Industrial &Production Engineering

 Example
• An OR study done for the San Francisco Police Department
resulted in the development of a computerized system for optimally
scheduling and deploying police patrol officers. The new system
provided annual savings of $11 million, an annual $3 million
increase in traffic citation revenues, and a 20 percent improvement
in response times.
• In assessing the appropriate objectives for this study, three
fundamental objectives were identified:
1. Maintain a high level of citizen safety.
2. Maintain a high level of officer morale.
3. Minimize the cost of operations.

Bangladesh University of Eng. & Tech. Slide 7 of 15 Industrial &Production Engineering

 Formulating a Mathematical Model
• After the problem is defined, the next phase is to
reformulate this problem in a form that is convenient for
analysis.
• Models are idealized representations.
• Models abstract the essence of the subject of inquiry,
showing interrelationships, and facilitating analysis.
• Mathematical models are also idealized representations,
but they are expressed in terms of mathematical
symbols and expressions.

Bangladesh University of Eng. & Tech. Slide 8 of 15 Industrial &Production Engineering

 Formulating a Mathematical Model

• In mathematical programming models, we have:

– Decision variables
– Objective functions
– Constraint functions
– Parameters

• Determining the appropriate values to assign to the parameters of

the model (one value per parameter) is both a critical and a
challenging part of the model-building process.
• Because of the uncertainty about the true value of the parameter, it
is important to analyze how the solution derived from the model
would change (if at all) if the value assigned to the parameter were
changed to other plausible values. This process is referred to as
sensitivity analysis.

Bangladesh University of Eng. & Tech. Slide 9 of 15 Industrial &Production Engineering

 Formulating a Mathematical Model
• Real problems normally don’t have just a single “right”
model.
• It is even possible that two or more completely different
types of models may be developed to help analyze the
same problem.
• A model is necessarily an abstract idealization of the
problem, so approximations and simplifying assumptions
generally are required if the model is to be tractable
(capable of being solved).
• It is required that there be a high correlation between the
prediction by the model and what would actually happen
in the real world.
Bangladesh University of Eng. & Tech. Slide 10 of 15 Industrial &Production Engineering
 Formulating a Mathematical Model
• In developing the model, a good approach is to begin
with a very simple version and then move in evolutionary
fashion toward more elaborate models that more nearly
reflect the complexity of the real problem.
• This process of model enrichment continues only as long
as the model remains tractable.
• The basic trade-off under constant consideration is
between the precision and the tractability of the model.
• If there are multiple objectives, their respective
measures commonly are then transformed and
combined into a composite measure, called the overall
measure of performance.
Bangladesh University of Eng. & Tech. Slide 11 of 15 Industrial &Production Engineering
 Deriving Solutions from the
Model
• After a mathematical model is formulated for the problem under
consideration, the next phase in an OR study is to develop a
procedure (usually a computer-based procedure) for deriving
solutions to the problem from this model.
• For experienced OR practitioners, finding a solution is the fun part,
whereas the real work comes in the preceding and following steps,
including the postoptimality analysis.
• Eminent management scientist and Nobel Laureate in economics
Herbert Simon points out that satisficing is much more prevalent
than optimizing in actual practice.
• Satisficing is a combination of the words satisfactory and optimizing.
• In the words of one of England’s OR leaders, Samuel Eilon,
“Optimizing is the science of the ultimate; satisficing is the art of the
feasible.”

Bangladesh University of Eng. & Tech. Slide 12 of 15 Industrial &Production Engineering

 Testing the Model

• Developing a large mathematical model is analogous in some

ways to developing a large computer program.
• This process of testing and improving a model to increase its
validity is commonly referred to as model validation.
• The group doing this review preferably should include at least
one individual who did not participate in the formulation of the
model.
• It is also useful to make sure that all the mathematical
expressions are dimensionally consistent in the units used.
• A more systematic approach to testing the model is to use a
retrospective test.
• Documenting the process used for model validation is important.
Bangladesh University of Eng. & Tech. Slide 13 of 15 Industrial &Production Engineering
 Preparing to Apply the Model

• What happens after the testing phase has been

completed and an acceptable model has been
developed?
• If the model is to be used repeatedly, the next step is to
install a well documented system for applying the model
as prescribed by management.
• This system will include the model, solution procedure
(including postoptimality analysis), and operating
procedure for implementation.

Bangladesh University of Eng. & Tech. Slide 14 of 15 Industrial &Production Engineering

 Implementation

• After a system is developed for applying the model, the

last phase of an OR study is to implement this system as
prescribed by management.
• This phase is a critical one because it is here, and only
here, that the benefits of the study are reaped.
• Good communications help to ensure that the study
accomplishes what management wanted and so
deserves implementation.

Bangladesh University of Eng. & Tech. Slide 15 of 15 Industrial &Production Engineering